The methods of integral equations numerical solving are proposed. These methods combine both deterministic and statistic operations. Like when using deterministic methods, the problem is reduced to solving a set of algebraic equations. But approximation of the integral by finite sum is performed by means of the Monte Carlo method.

In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...

let $f$ be a finite extension of $bbb q$‎, ‎${bbb q}_p$ or a global‎ ‎field of positive characteristic‎, ‎and let $e/f$ be a galois extension‎. ‎we study the realization fields of‎ ‎finite subgroups $g$ of $gl_n(e)$ stable under the natural‎ ‎operation of the galois group of $e/f$‎. ‎though for sufficiently large $n$ and a fixed‎ algebraic number field $f$ every its finite extension $e$ is‎ ‎re...

This article introduces a numerical method based on an M(n+ 1) set of general, hybrid orthonormal Bernstein functions coupled with Block-Pulse Functions(HOBB) on the interval [0,1] for approximating solutions of a Coupled System of linear and non linear Volterra integral and Integro-Differential equations. This method reduces a Coupled System of Volterra integral and IntegroDifferential equatio...

Some new approximation methods are proposed for the numerical evaluation of the finitepart singular integral equations defined on Hilbert spaces when their singularity consists of a homeomorphism of the integration interval, which is a unit circle, on itself. Therefore, some existence theorems are proved for the solutions of the finite-part singular integral equations, approximated by several s...

In this paper, efficient numerical techniques have been proposed to solve nonlinear Hammerstein fuzzy integral equations. The proposed methods are based on Bernstein polynomials and Legendre wavelets approximation. Usually, nonlinear fuzzy integral equations are very difficult to solve both analytically and numerically. The present methods applied to the integral equations is reduced to solve t...

WAVEFORM RELAXATION METHODS OF NONLINEAR INTEGRAL-DIFFERENTIAL-ALGEBRAIC EQUATIONS ∗1) Yao-lin Jiang (Department of Mathematical Sciences, Xi’an Jiaotong University, Xi’an 710049, China) Abstract In this paper we consider continuous-time and discrete-time waveform relaxation methods for general nonlinear integral-differential-algebraic equations. For the continuous-time case we derive the conve...

An effective method based upon Alpert multiwavelets is proposed for the solution of Hallen’s integral equation. The properties of Alpert multiwavelets are first given. These wavelets are utilized to reduce the solution of Hallen’s integral equation to the solution of sparse algebraic equations. In order to save memory requirement and computation time, a threshold procedure is applied to obtain ...

A numerical method to solve nonlinear Fredholm integral equations of second kind is presented in this work. The method is based upon hybrid function approximate. The properties of hybrid of block-pulse functions and Taylor series are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of algebraic equations. Some numerical examples are selec...

In this paper, the linear semiorthogonal compactly supported B-spline wavelets together with their dual wavelets have been applied to approximate the solutions of Fredholm integral equations of the second kind. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. The method is computatio...